We consider a two-competitor/one-prey model in which both competitors exhibit a general functional response and one of the competitors exhibits a density-dependent mortality rate. It is shown that the two competitors can coexist upon the single prey.As an example, we consider a two-competitor/one-prey model with a Holling II functional response. Our results demonstrate that density-dependent mortality in one of the competitors can prevent competitive exclusion. Moreover, by constructing a Liapunov function, the system has a globally stable positive equilibrium.

The microquasar GRS 1915+105, exhibits a large variety of characteristic states, according to its luminosity, spectral state, and variability. The most interesting one is the so-called ρ-state, whose light curve shows recurrent bursts. This paper presents a model based on Fitzhugh-Nagumo equations containing two variables: x, linked to the source photon emission rate detected by the MECS, and y related to the mean photon energy. We aim at providing a simple mathematical framework composed by non-linear differential equations useful to predict the observed light curve and the energy lags for the ρ-state and possibly other classes of the source. We studied the equilibrium state and the stability conditions of this system that includes one external parameter, J, that can be considered a function of the disk accretion rate. Our work is based on observations performed with the MECS on board BeppoSAX when the source was in ρ and ν mode, respectively. The evolution of the mean count rate and photon energy were derived from a study of the trajectories in the count rate-photon energy plane. Assuming J constant, we found a solution that reproduces the x profile of the ρ class bursts and, unexpectedly, we found that y exhibited a time modulation similar to that of the mean energy. Moreover, assuming a slowly modulated J the solutions for x quite similar to those observed in the ν class light curves is reproduced. According these results, the outer mass accretion rate is probably responsible for the state transitions, but within the ρ-class it is constant. This finding makes stronger the heuristic meaning of the non-linear model and suggests a simple relation between the variable x and y. However, how a system of dynamical equations can be derived from the complex mathematical apparatus of accretion disks remains to be furtherly explored. © 2014 Springer Science+Business Media Dordrecht

Lyapunov functions are given to prove the global asymptotic stability of a large class of predator-prey models, including the ones in which the intrinsic growth rate of the prey follows the Ricker-law or the Odell generalization of the logistic law, and the functional predator response is of Holling type.

An acidic peroxidase (EC 1.11.1.7) produced by cell suspension cultures of Cassia didymobotrya (wild senna) was purified from culture medium collected on the 29th day. The enzyme was shown to be a glycoprotein with a pI of 3.5, a molecular mass of approx. 43 kDa by SDS/PAGE and 50 kDa by gel filtration. The N-terminal sequence was very similar to those of other plant peroxidases. The peroxidase was characterized by a high specificity towards coniferyl alcohol and other natural phenolics such as guaiacol and ferulic and caffeic acids. These findings suggest that the enzyme is involved in lignification processes of the cell wall. Moreover, the enzyme was able to catalyse the oxidation of 4,3',4'-trihydroxychalcone and 4, 3',4'-trihydroxy-3-methoxychalcone to the corresponding 3, 3'-biflavanones, as mixtures of racemic and meso forms.

Resorcinarene octamethyl ethers, bearing carboalkyloxy groups in the side chains, have been shown to interact with FeIII in organic media. 1H‐NMR studies, carried out using GaIII instead of FeIII, suggest that these systems have two active sites of interaction, the first located at the aromatic moiet and the other in the vicinity of the carbonyl groups. As a confirmation of this, resorcinarenes without carbonyl groups in the side chains have been found to exhibit only one active site. Notably, in the latter case the interaction results in configurational changes.